Quantum Gases In Low Dimensions

The book addresses several aspects of thermodynamics and correlations in the strongly-interacting regime of one-dimensional bosons, a topic at the forefront of current theoretical and experimental studies. Strongly correlated systems of one-dimensional bosons have a long history of theoretical study. Their experimental realisation in ultracold atom experiments is the subject of current research, which took off in the early 2000s. Yet these experiments raise new theoretical questions, just begging to be answered. Correlation functions are readily available for experimental measurements. In this book, they are tackled by means of sophisticated theoretical methods developed in condensed matter physics and mathematical physics, such as bosonization, the Bethe Ansatz and conformal field theory. Readers are introduced to these techniques, which are subsequently used to investigate many-body static and dynamical correlation functions.

This volume provides a broad overview of the principal theoretical techniques applied to non-equilibrium and finite temperature quantum gases. Covering Bose-Einstein condensates, degenerate Fermi gases, and the more recently realised exciton-polariton condensates, it fills a gap by linking between different methods with origins in condensed matter physics, quantum field theory, quantum optics, atomic physics, and statistical mechanics.

Quantum phenomena of many-particle systems are fascinating in their complexity and are consequently not fully understood and largely untapped in terms of practical applications. Ultracold gases provide a unique platform to build up model systems of quantum many-body physics with highly controlled microscopic constituents. In this way, many-body quantum phenomena can be investigated with an unprecedented level of precision, and control and models that cannot be solved with present day computers may be studied using ultracold gases as a quantum simulator.This book addresses the need for a comprehensive description of the most important advanced experimental methods and techniques that have been developed along with the theoretical framework in a clear and applicable format. The focus is on methods that are especially crucial in probing and understanding the many-body nature of the quantum phenomena in ultracold gases and most topics are covered both from a theoretical and experimental viewpoint, with interrelated chapters written by experts from both sides of research.Graduate students and post-doctoral researches working on ultracold gases will benefit from this book, as well as researchers from other fields who wish to gain an overview of the recent fascinating developments in this very dynamically evolving field. Sufficient level of both detailed high level research and a pedagogical approach is maintained throughout the book so as to be of value to those entering the field as well as advanced researchers. Furthermore, both experimentalists and theorists will benefit from the book; close collaboration between the two are continuously driving the field to a very high level and will be strengthened to continue the important progress yet to be made in the field.

The Enrico Fermi summer school on Quantum Matter at Ultralow Temperatures held on 7-15 July 2014 at Varenna, Italy, featured important frontiers in the field of ultracold atoms. For the last 25 years, this field has undergone dramatic developments, which were chronicled by several Varenna summer schools, in 1991 on Laser Manipulation of Atoms, in 1998 on Bose-Einstein Condensation in Atomic Gases, and in 2006 on Ultra-cold Fermi Gases. The theme of the 2014 school demonstrates that the field has now branched out into many different directions, where the tools and precision of atomic physics are used to realise new quantum systems, or in other words, to quantum-engineer interesting Hamiltonians. The topics of the school identify major new directions: Quantum gases with long range interactions, either due to strong magnetic dipole forces, due to Rydberg excitations, or, for polar molecules, due to electric dipole interactions; quantum gases in lower dimensions; quantum gases with disorder; atoms in optical lattices, now with single-site optical resolution; systems with non-trivial topological properties, e.g. with spin-orbit coupling or in artificial gauge fields; quantum impurity problems (Bose and Fermi polarons); quantum magnetism. Fermi gases with strong interactions, spinor Bose-Einstein condensates and coupled multi-component Bose gases or Bose-Fermi mixtures continue to be active areas. The current status of several of these areas is systematically summarized in this volume.

This thesis explores the physics of non-equilibrium quantum dynamics in homogeneous two-dimensional (2D) quantum gases. Ultracold quantum gases driven out of equilibrium have been prominent platforms for studying quantum many-body physics. However, probing non-equilibrium dynamics in conventionally trapped, inhomogeneous atomic quantum gases has been a challenging task because coexisting mass transport and spreading of quantum correlations often complicate experimental analyses. In this work, the author solves this technical hurdle by producing ultracold cesium atoms in a quasi-2D optical box potential. The exquisite optical trap allows one to remove density inhomogeneity in a degenerate quantum gas and control its dimensionality. The author also details the development of a high-resolution, in situ imaging technique to monitor the evolution of collective excitations and quantum transport down to atomic shot-noise, and at the length scale of elementary collective excitations. Meanwhile, tunable Feshbach resonances in ultracold cesium atoms permit precise and dynamical control of interactions with high temporal and even spatial resolutions. By employing these state-of-the-art techniques, the author performed interaction quenches to control the generation and evolution of quasiparticles in quantum gases, presenting the first direct measurement of quantum entanglement between interaction quench generated quasiparticle pairs in an atomic superfluid. Quenching to attractive interactions, this work shows stimulated emission of quasiparticles, leading to amplified density waves and fragmentation, forming 2D matter-wave Townes solitons that were previously considered impossible to form in equilibrium due to their instability. This thesis unveils a set of scale-invariant and universal quench dynamics and provides unprecedented tools to explore quantum entanglement transport in a homogenous quantum gas.

This thesis develops new techniques for simulating the low-energy behaviour of quantum spin systems in one and two dimensions. Combining these developments, it subsequently uses the formalism of tensor network states to derive an effective particle description for one- and two-dimensional spin systems that exhibit strong quantum correlations. These techniques arise from the combination of two themes in many-particle physics: (i) the concept of quasiparticles as the effective low-energy degrees of freedom in a condensed-matter system, and (ii) entanglement as the characteristic feature for describing quantum phases of matter. Whereas the former gave rise to the use of effective field theories for understanding many-particle systems, the latter led to the development of tensor network states as a description of the entanglement distribution in quantum low-energy states.

The rapidly developing topic of ultracold atoms has many actual and potential applications for condensed-matter science, and the contributions to this book emphasize these connections. Ultracold Bose and Fermi quantum gases are introduced at a level appropriate for first-year graduate students and non-specialists such as more mature general physicists. The reader will find answers to questions like: how are experiments conducted and how are the results interpreted? What are the advantages and limitations of ultracold atoms in studying many-body physics? How do experiments on ultracold atoms facilitate novel scientific opportunities relevant to the condensed-matted community? This volume seeks to be comprehensible rather than comprehensive; it aims at the level of a colloquium, accessible to outside readers, containing only minimal equations and limited references. In large part, it relies on many beautiful experiments from the past fifteen years and their very fruitful interplay with basic theoretical ideas. In this particular context, phenomena most relevant to condensed-matter science have been emphasized. Introduces ultracold Bose and Fermi quantum gases at a level appropriate for non-specialists Discusses landmark experiments and their fruitful interplay with basic theoretical ideas Comprehensible rather than comprehensive, containing only minimal equations